12 citations · 21 across the 3 of their papers we have counts for
3 papers
math.NT2008★ 12 cited
Rational points in periodic analytic sets and the Manin-Mumford conjecture
Jonathan Pila, Umberto Zannier
We present a new proof of the Manin-Mumford conjecture about torsion points on algebraic subvarieties of abelian varieties. Our principle, which admits other applications, is to vi…
math.NT2005★ 1 cited
Note on the rational points of a pfaff curve
Jonathan Pila
Let X be the graph in the plane of a pfaffian function f (in the sense of Khovanskii). Suppose X is not algebraic. This note gives an upper bound for the number of rational points…
math.NT2005★ 8 cited
Counting points on curves over families in polynomial time
Jonathan Pila
This note concerns the theoretical algorithmic problem of counting rational points on curves over finite fields. It explicates how the algorithmic scheme introduced by Schoof and g…